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51. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 11 > Issue: 3
LIBROS RECIBIDOS / BOOKS RECEIVED
52. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 11 > Issue: 3
Enric Trillas Menger’s Trace in Fuzzy Logic
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This paper deals with the relation with Fuzzy Logic of some of the ideas of Karl Menger published between 1942 and 1966 and concerning what he called “Hazy Sets”, Probabilistic Relations and Statistical Metric Spaces. The author maintains the opinion that if Lofti A. Zadeh is actually the father of Fuzzy Logic, Menger not only was a forerunner of this field but that his ideas were and still are influential on it.
53. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 11 > Issue: 3
SUMARIO DEL VOL. XI / CONTENTS OF VOL. XI
54. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 11 > Issue: 3
Ilie Parvu The Unity of Scientific Knowledge in the Framework of a Typological Approach of Theories
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The paper proposes a typology of the scientific theories based on the modality of mathematizing (relying on the kind of mathematics which participates to the theory edification and the level of mathematical organizing of the theoretical frame). This gives us, like the classification of the geometries from the famous -Erlagen Program- initiated by Felix Klein, an internal principle for the connection of the different forms or levels of the theorizing, a constructive basis for the understanding of the complex structural nets of the mature scientific disciplines.
55. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 11 > Issue: 3
Adrian Miroiu Global Warming and Moral Theorizing
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The aim of my paper is to explore in some detail some epistemological issues concerning moral theorizing on global warming. First, I consider the issue of the structure of the theoretical approach in a field of inquiry requiring normative assessments. How do theoretical principles work here? What is to be regarded as a normative evidence for such a theory? Second, the criteria to determine which part, if any, of the theory gets normatively constrained, and which does not, are discussed. Third, I focus on the procedures to reach an equilibrium between such a theory and its evidence and to reach it, changes might be required on the normative side of the theory, rather than on its non-normative one
56. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 11 > Issue: 3
Mircea Flonta Does the Scientific Paper Accurately Mirror the Very Grounds of Scientific Assessment?
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This paper presents aprevalent representation about the objectivity and impartiality of scientific knowledge that emerges from the structure and style of the standard research paper. This representation is critically examined considering some rather untypical scientific papers reporting controversies between researchers in a certain field of experimental science. The role of personal preconceptions and intellectual prejudices in the assessment of scientific theories is emphasized by reference to Einsteinls grounds for his general theory of relativity.
57. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 12 > Issue: 1
Francisco Rodriguez Consuegra Nominal definitions and logical consequence in the Peano School
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This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) asa result of their conception of nominal definitions. Also, their semantic definition of logical consequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of theexpression “nominal definition” are presented first. Second, the main advantages of this kind of definition, as they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logicalconsequence.
58. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 12 > Issue: 1
Gregory H. Moore Hilbert and the emergence of modern mathematical logic
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Hilbert’s unpublished 1917 lectures on logic, analyzed here, are the beginning of modern metalogic. In them he proved the consistency and Post-completeness (maximal consistency) of propositional logic -results traditionally credited to Bernays (1918) and Post (1921). These lectures contain the first formal treatment of first-order logic and form the core of Hilbert’s famous 1928 book with Ackermann. What Bernays, influenced by those lectures, did in 1918 was to change the emphasis from the consistency and Post-completeness of a logic to its soundness and completeness: a sentence is provable if and only if valid. By 1917, strongly influenced by PM, Hilbert accepted the theory of types and logicism -a surprising shift. But by 1922 he abandoned the axiom of reducibility and then drew back from logicism, returning to his 1905 approach of trying to prove the consistency of number theory syntactically.
59. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 12 > Issue: 1
LIBROS RECIBIDOS / BOOKS RECEIVED
60. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 12 > Issue: 1
José Ferreiros Notes on types, sets, and logicism, 1930-1950
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The present paper is a contribution to the history of logic and its philosophy toward the mid-20th century. It examines the interplay between logic, type theory and set theory during the 1930s and 40s, before the reign of first-order logic, and the closely connected issue of the fate of logicism. After a brief presentation of the emergence of logicism, set theory, and type theory (with particular attention to Carnap and Tarski), Quine’s work is our central concern, since he was seemingly the most outstanding logicist around 1940, though he would shortly abandon that viewpoint and promote first-order logic as all of logic. Quine’s class-theoretic systems NF and ML, and his farewell to logicism, are examined. The last section attempts to summarize the motives why set theory was preferred to other systems, and first orderlogic won its position as the paradigm logic system after the great War.